求解弹性波有限差分法中自由边界处理方法的对比
|
摘要
自由边界条件在计算方法中的数值表征是地震波模拟中的一个重要内容,表征的有效性直接关系到所得波场能否代表地表介质特性的真实响应。该文评估了交错网格有限差分法中5种常用自由边界处理方法:直接法、应力镜像法、改进应力镜像法、横向各向同性介质替换法和声学边界替换法,并与有限元法模拟结果进行了对比,波形曲线直观比较及波幅比与相关系数定量比较显示横向各向同性介质替换法与有限法模拟结果一致性最好。进一步的层状介质模型弹性波数值模拟结果表明:横向各向同性介质替换法的精度和可靠性最高,能真实表征地表介质中的地震波传播。
Representation of free-surface boundary condition in numerical calculations is an important aspect for seismic wave simulation.The effectiveness of numerical representation directly relates to whether the wave field can represent the true response of free-surface medium characteristics.Five common implementations of free-surface boundary used in the staggered-grid finite-difference method were evaluated,including the direct method,the stress image method,the improved stress image method,the transversely isotropic medium approach and the acoustic-elastic boundary approach,and a comparison with the finite-element method was also conducted.Simulation results of the transversely isotropic medium approach and the finite-element method are consistent best in visual comparison of waveform curve and quantitative comparison of amplitude ratio and correlation coefficient.Further numerical simulation results of elastic wave in layered medium model show that the transversely isotropic medium approach is the most accurate and reliable one which could represent seismic wave propagation in free-surface medium.
Representation of free-surface boundary condition in numerical calculations is an important aspect for seismic wave simulation.The effectiveness of numerical representation directly relates to whether the wave field can represent the true response of free-surface medium characteristics.Five common implementations of free-surface boundary used in the staggered-grid finite-difference method were evaluated,including the direct method,the stress image method,the improved stress image method,the transversely isotropic medium approach and the acoustic-elastic boundary approach,and a comparison with the finite-element method was also conducted.Simulation results of the transversely isotropic medium approach and the finite-element method are consistent best in visual comparison of waveform curve and quantitative comparison of amplitude ratio and correlation coefficient.Further numerical simulation results of elastic wave in layered medium model show that the transversely isotropic medium approach is the most accurate and reliable one which could represent seismic wave propagation in free-surface medium.
引文
[1]Virieux J.P-SV wave propagation in heterogeneousmedia:Velocity-stress finite-difference method[J].Geophysics,1986,51(4):889―901.
[2]Graves R W.Simulating seismic wave propagation in 3Delastic media using staggered-grid finite differences[J].Bulletin of the Seismological Society of America,1996,86(4):1091―1106.
[3]董良国,马在田,曹景忠,等.一阶弹性波方程交错网格高阶差分解法[J].地球物理学报,2000,43(3):411―419.Dong Liangguo,Ma Zaitian,Cao Jingzhong,et al.Astaggered-grid high-order difference method of one-orderelastic wave equation[J].Chinese Journal of Geophysics,2000,43(3):411―419.(in Chinese)
[4]宋爽.时域有限差分方法用于浅地层弹性波场模拟[D].北京:北京大学,2008.Song Shuang.Numerical simulation of elastic wavepropagation in shallow strata using FDTD method[D].Beijing:Peking University,2008.(in Chinese)
[5]汪利民.三维带地形瑞雷面波交错网格有限差分发正演技术研究[D].武汉:中国地质大学,2009.Wang Limin.Modeling of rayleigh-wave propagation inthree-dimensional media with topography usingstaggered-grid finite difference scheme[D].Wuhan:China University of Geosciences,2009.(in Chinese)
[6]王秀明,张海澜.用于具有不规则起伏自由表面的介质中弹性波模拟的有限差分算法[J].中国科学(G辑),2004,34(5):481―493.Wang Xiuming,Zhang Hailan.Modeling the seismicwave in the media with irregular free interface by thefinite-difference method[J].Science in China(Series G),2004,34(5):481―493.(in Chinese)
[7]裴正林.任意起伏地表弹性波方程交错网格高阶有限差分法数值模拟[J].石油地球物理勘探,2004,39(6):629―634.Pei Zhenglin.Numerical modeling using staggered-gridhigh-order finite-difference of elastic wave equation onarbitrary relief surface[J].Oil Geophysical Prospecting,2004,39(6):629―634.(in Chinese)
[8]唐圣松.起伏二维地表模型瑞雷波场正演研究[D].长沙:中南大学,2009.Tang Shengsong.Study on Rayleigh-wave field forwardof two-dimensional rolling ground model[D].Changsha:Central South University,2009.(in Chinese)
[9]周竹生,刘喜亮,熊孝雨.弹性介质中瑞雷面波有限差分法正演模拟[J].地球物理学报,2007,50(2):567―573.Zhou Zhusheng,Liu Xiliang,Xiong Xiaoyu.Finite-difference modeling of Rayleigh surface wave inelastic media[J].Chinese Journal of Geophysics,2007,50(2):567―573.(in Chinese)
[10]王雪秋,孙建国.地震波有限差分数值模拟框架下的起伏地表处理方法综述[J].地球物理学进展,2008,23(1):40―48.Wang Xueqiu,Sun Jianguo.The state-of-the-art innumerical modeling includingsurface topography withfinite-difference method[J].Progress in Geophysics,2008,23(1):40―48.(in Chinese)
[11]张华,李振春,韩文功.起伏地表条件下地震波数值模拟方法综述[J].勘探地球物理进展,2007,30(5):334―339.Zhang Hua,Li Zhenchun,Han Wengong.Review ofseismic wave numerical simulation from irregulartopography[J].Progress in Exploration Geophysics,2007,30(5):334―339.(in Chinese)
[12]Mittet R.Free-surface boundary conditions for elasticstaggered-grid modeling schemes[J].Geophysics,2002,67(5):1616―1623.
[13]Xu Yixian,Xia Jianghai,Richard D Miller.Numericalinvestigation of implementation of air-earth boundary byacoustic-elastic boundary approach[J].Geophysics,2007,72(5):SM147―SM153.
[14]Kosloff D,Kessler D,Filho A Q,et al.Solution of theequation of dynamic elasticity by a Chebychev spectralmethod[J].Geophysics,1990,55(6):734―748.
[15]Robertsson J O.A numerical free-surface condition forelastic/viscoelastic finite-difference modeling in thepresence of topography[J].Geophysics,1996,61(6):1921―1934.
[16]Levander A R.Fourth-order finite-difference P-SVseismograms[J].Geophysics,1988,53(11):1425―1436.
[17]牟永光,裴正林.三维复杂介质地震波数值模拟[M].北京:石油工业出版社,2005.Mou Yongguang,Pei Zhenglin.Seismic numericalmodeling for 3-D complex media[M].Beijing:Petroleum Industry Press,2005.(in Chinese)
[2]Graves R W.Simulating seismic wave propagation in 3Delastic media using staggered-grid finite differences[J].Bulletin of the Seismological Society of America,1996,86(4):1091―1106.
[3]董良国,马在田,曹景忠,等.一阶弹性波方程交错网格高阶差分解法[J].地球物理学报,2000,43(3):411―419.Dong Liangguo,Ma Zaitian,Cao Jingzhong,et al.Astaggered-grid high-order difference method of one-orderelastic wave equation[J].Chinese Journal of Geophysics,2000,43(3):411―419.(in Chinese)
[4]宋爽.时域有限差分方法用于浅地层弹性波场模拟[D].北京:北京大学,2008.Song Shuang.Numerical simulation of elastic wavepropagation in shallow strata using FDTD method[D].Beijing:Peking University,2008.(in Chinese)
[5]汪利民.三维带地形瑞雷面波交错网格有限差分发正演技术研究[D].武汉:中国地质大学,2009.Wang Limin.Modeling of rayleigh-wave propagation inthree-dimensional media with topography usingstaggered-grid finite difference scheme[D].Wuhan:China University of Geosciences,2009.(in Chinese)
[6]王秀明,张海澜.用于具有不规则起伏自由表面的介质中弹性波模拟的有限差分算法[J].中国科学(G辑),2004,34(5):481―493.Wang Xiuming,Zhang Hailan.Modeling the seismicwave in the media with irregular free interface by thefinite-difference method[J].Science in China(Series G),2004,34(5):481―493.(in Chinese)
[7]裴正林.任意起伏地表弹性波方程交错网格高阶有限差分法数值模拟[J].石油地球物理勘探,2004,39(6):629―634.Pei Zhenglin.Numerical modeling using staggered-gridhigh-order finite-difference of elastic wave equation onarbitrary relief surface[J].Oil Geophysical Prospecting,2004,39(6):629―634.(in Chinese)
[8]唐圣松.起伏二维地表模型瑞雷波场正演研究[D].长沙:中南大学,2009.Tang Shengsong.Study on Rayleigh-wave field forwardof two-dimensional rolling ground model[D].Changsha:Central South University,2009.(in Chinese)
[9]周竹生,刘喜亮,熊孝雨.弹性介质中瑞雷面波有限差分法正演模拟[J].地球物理学报,2007,50(2):567―573.Zhou Zhusheng,Liu Xiliang,Xiong Xiaoyu.Finite-difference modeling of Rayleigh surface wave inelastic media[J].Chinese Journal of Geophysics,2007,50(2):567―573.(in Chinese)
[10]王雪秋,孙建国.地震波有限差分数值模拟框架下的起伏地表处理方法综述[J].地球物理学进展,2008,23(1):40―48.Wang Xueqiu,Sun Jianguo.The state-of-the-art innumerical modeling includingsurface topography withfinite-difference method[J].Progress in Geophysics,2008,23(1):40―48.(in Chinese)
[11]张华,李振春,韩文功.起伏地表条件下地震波数值模拟方法综述[J].勘探地球物理进展,2007,30(5):334―339.Zhang Hua,Li Zhenchun,Han Wengong.Review ofseismic wave numerical simulation from irregulartopography[J].Progress in Exploration Geophysics,2007,30(5):334―339.(in Chinese)
[12]Mittet R.Free-surface boundary conditions for elasticstaggered-grid modeling schemes[J].Geophysics,2002,67(5):1616―1623.
[13]Xu Yixian,Xia Jianghai,Richard D Miller.Numericalinvestigation of implementation of air-earth boundary byacoustic-elastic boundary approach[J].Geophysics,2007,72(5):SM147―SM153.
[14]Kosloff D,Kessler D,Filho A Q,et al.Solution of theequation of dynamic elasticity by a Chebychev spectralmethod[J].Geophysics,1990,55(6):734―748.
[15]Robertsson J O.A numerical free-surface condition forelastic/viscoelastic finite-difference modeling in thepresence of topography[J].Geophysics,1996,61(6):1921―1934.
[16]Levander A R.Fourth-order finite-difference P-SVseismograms[J].Geophysics,1988,53(11):1425―1436.
[17]牟永光,裴正林.三维复杂介质地震波数值模拟[M].北京:石油工业出版社,2005.Mou Yongguang,Pei Zhenglin.Seismic numericalmodeling for 3-D complex media[M].Beijing:Petroleum Industry Press,2005.(in Chinese)
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心